Approximation of Potential Energy Surfaces with Spherical Harmonics.

In this note we detail a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling potential energy surfaces. Our presentation builds and expands on (Drautz, Phys. Rev. B 99, 2019). We clarify how to modify this construction to guarantee that the basis becomes complete, and moreover show how to obtain an orthogonal basis.